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TRS Standard pair #516961085
details
property
value
status
complete
benchmark
aprove3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
9.7167289257 seconds
cpu usage
10.997605948
max memory
6.34376192E8
stage attributes
key
value
output-size
29530
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) DependencyGraphProof [EQUIVALENT, 0 ms] (32) QDP (33) UsableRulesProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) TransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) TransformationProof [EQUIVALENT, 0 ms] (42) QDP (43) QDPOrderProof [EQUIVALENT, 23 ms] (44) QDP (45) DependencyGraphProof [EQUIVALENT, 0 ms] (46) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: function(iszero, 0, dummy, dummy2) -> true function(iszero, s(x), dummy, dummy2) -> false function(p, 0, dummy, dummy2) -> 0 function(p, s(0), dummy, dummy2) -> 0 function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x)) function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y) function(if, true, x, y) -> y function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y)) function(third, x, y, z) -> z Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: function(iszero, 0, dummy, dummy2) -> true function(iszero, s(x), dummy, dummy2) -> false function(p, 0, dummy, dummy2) -> 0 function(p, s(0), dummy, dummy2) -> 0 function(p, s(s(x)), dummy, dummy2) -> s(function(p, s(x), x, x)) function(plus, dummy, x, y) -> function(if, function(iszero, x, x, x), x, y) function(if, true, x, y) -> y function(if, false, x, y) -> function(plus, function(third, x, y, y), function(p, x, x, y), s(y))
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